1 SUBROUTINE ZUNGQL( M, N, K, A, LDA, TAU, WORK, LWORK, INFO )
2 *
3 * -- LAPACK routine (version 3.2) --
4 * -- LAPACK is a software package provided by Univ. of Tennessee, --
5 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
6 * November 2006
7 *
8 * .. Scalar Arguments ..
9 INTEGER INFO, K, LDA, LWORK, M, N
10 * ..
11 * .. Array Arguments ..
12 COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
13 * ..
14 *
15 * Purpose
16 * =======
17 *
18 * ZUNGQL generates an M-by-N complex matrix Q with orthonormal columns,
19 * which is defined as the last N columns of a product of K elementary
20 * reflectors of order M
21 *
22 * Q = H(k) . . . H(2) H(1)
23 *
24 * as returned by ZGEQLF.
25 *
26 * Arguments
27 * =========
28 *
29 * M (input) INTEGER
30 * The number of rows of the matrix Q. M >= 0.
31 *
32 * N (input) INTEGER
33 * The number of columns of the matrix Q. M >= N >= 0.
34 *
35 * K (input) INTEGER
36 * The number of elementary reflectors whose product defines the
37 * matrix Q. N >= K >= 0.
38 *
39 * A (input/output) COMPLEX*16 array, dimension (LDA,N)
40 * On entry, the (n-k+i)-th column must contain the vector which
41 * defines the elementary reflector H(i), for i = 1,2,...,k, as
42 * returned by ZGEQLF in the last k columns of its array
43 * argument A.
44 * On exit, the M-by-N matrix Q.
45 *
46 * LDA (input) INTEGER
47 * The first dimension of the array A. LDA >= max(1,M).
48 *
49 * TAU (input) COMPLEX*16 array, dimension (K)
50 * TAU(i) must contain the scalar factor of the elementary
51 * reflector H(i), as returned by ZGEQLF.
52 *
53 * WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK))
54 * On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
55 *
56 * LWORK (input) INTEGER
57 * The dimension of the array WORK. LWORK >= max(1,N).
58 * For optimum performance LWORK >= N*NB, where NB is the
59 * optimal blocksize.
60 *
61 * If LWORK = -1, then a workspace query is assumed; the routine
62 * only calculates the optimal size of the WORK array, returns
63 * this value as the first entry of the WORK array, and no error
64 * message related to LWORK is issued by XERBLA.
65 *
66 * INFO (output) INTEGER
67 * = 0: successful exit
68 * < 0: if INFO = -i, the i-th argument has an illegal value
69 *
70 * =====================================================================
71 *
72 * .. Parameters ..
73 COMPLEX*16 ZERO
74 PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ) )
75 * ..
76 * .. Local Scalars ..
77 LOGICAL LQUERY
78 INTEGER I, IB, IINFO, IWS, J, KK, L, LDWORK, LWKOPT,
79 $ NB, NBMIN, NX
80 * ..
81 * .. External Subroutines ..
82 EXTERNAL XERBLA, ZLARFB, ZLARFT, ZUNG2L
83 * ..
84 * .. Intrinsic Functions ..
85 INTRINSIC MAX, MIN
86 * ..
87 * .. External Functions ..
88 INTEGER ILAENV
89 EXTERNAL ILAENV
90 * ..
91 * .. Executable Statements ..
92 *
93 * Test the input arguments
94 *
95 INFO = 0
96 LQUERY = ( LWORK.EQ.-1 )
97 IF( M.LT.0 ) THEN
98 INFO = -1
99 ELSE IF( N.LT.0 .OR. N.GT.M ) THEN
100 INFO = -2
101 ELSE IF( K.LT.0 .OR. K.GT.N ) THEN
102 INFO = -3
103 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
104 INFO = -5
105 END IF
106 *
107 IF( INFO.EQ.0 ) THEN
108 IF( N.EQ.0 ) THEN
109 LWKOPT = 1
110 ELSE
111 NB = ILAENV( 1, 'ZUNGQL', ' ', M, N, K, -1 )
112 LWKOPT = N*NB
113 END IF
114 WORK( 1 ) = LWKOPT
115 *
116 IF( LWORK.LT.MAX( 1, N ) .AND. .NOT.LQUERY ) THEN
117 INFO = -8
118 END IF
119 END IF
120 *
121 IF( INFO.NE.0 ) THEN
122 CALL XERBLA( 'ZUNGQL', -INFO )
123 RETURN
124 ELSE IF( LQUERY ) THEN
125 RETURN
126 END IF
127 *
128 * Quick return if possible
129 *
130 IF( N.LE.0 ) THEN
131 RETURN
132 END IF
133 *
134 NBMIN = 2
135 NX = 0
136 IWS = N
137 IF( NB.GT.1 .AND. NB.LT.K ) THEN
138 *
139 * Determine when to cross over from blocked to unblocked code.
140 *
141 NX = MAX( 0, ILAENV( 3, 'ZUNGQL', ' ', M, N, K, -1 ) )
142 IF( NX.LT.K ) THEN
143 *
144 * Determine if workspace is large enough for blocked code.
145 *
146 LDWORK = N
147 IWS = LDWORK*NB
148 IF( LWORK.LT.IWS ) THEN
149 *
150 * Not enough workspace to use optimal NB: reduce NB and
151 * determine the minimum value of NB.
152 *
153 NB = LWORK / LDWORK
154 NBMIN = MAX( 2, ILAENV( 2, 'ZUNGQL', ' ', M, N, K, -1 ) )
155 END IF
156 END IF
157 END IF
158 *
159 IF( NB.GE.NBMIN .AND. NB.LT.K .AND. NX.LT.K ) THEN
160 *
161 * Use blocked code after the first block.
162 * The last kk columns are handled by the block method.
163 *
164 KK = MIN( K, ( ( K-NX+NB-1 ) / NB )*NB )
165 *
166 * Set A(m-kk+1:m,1:n-kk) to zero.
167 *
168 DO 20 J = 1, N - KK
169 DO 10 I = M - KK + 1, M
170 A( I, J ) = ZERO
171 10 CONTINUE
172 20 CONTINUE
173 ELSE
174 KK = 0
175 END IF
176 *
177 * Use unblocked code for the first or only block.
178 *
179 CALL ZUNG2L( M-KK, N-KK, K-KK, A, LDA, TAU, WORK, IINFO )
180 *
181 IF( KK.GT.0 ) THEN
182 *
183 * Use blocked code
184 *
185 DO 50 I = K - KK + 1, K, NB
186 IB = MIN( NB, K-I+1 )
187 IF( N-K+I.GT.1 ) THEN
188 *
189 * Form the triangular factor of the block reflector
190 * H = H(i+ib-1) . . . H(i+1) H(i)
191 *
192 CALL ZLARFT( 'Backward', 'Columnwise', M-K+I+IB-1, IB,
193 $ A( 1, N-K+I ), LDA, TAU( I ), WORK, LDWORK )
194 *
195 * Apply H to A(1:m-k+i+ib-1,1:n-k+i-1) from the left
196 *
197 CALL ZLARFB( 'Left', 'No transpose', 'Backward',
198 $ 'Columnwise', M-K+I+IB-1, N-K+I-1, IB,
199 $ A( 1, N-K+I ), LDA, WORK, LDWORK, A, LDA,
200 $ WORK( IB+1 ), LDWORK )
201 END IF
202 *
203 * Apply H to rows 1:m-k+i+ib-1 of current block
204 *
205 CALL ZUNG2L( M-K+I+IB-1, IB, IB, A( 1, N-K+I ), LDA,
206 $ TAU( I ), WORK, IINFO )
207 *
208 * Set rows m-k+i+ib:m of current block to zero
209 *
210 DO 40 J = N - K + I, N - K + I + IB - 1
211 DO 30 L = M - K + I + IB, M
212 A( L, J ) = ZERO
213 30 CONTINUE
214 40 CONTINUE
215 50 CONTINUE
216 END IF
217 *
218 WORK( 1 ) = IWS
219 RETURN
220 *
221 * End of ZUNGQL
222 *
223 END
2 *
3 * -- LAPACK routine (version 3.2) --
4 * -- LAPACK is a software package provided by Univ. of Tennessee, --
5 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
6 * November 2006
7 *
8 * .. Scalar Arguments ..
9 INTEGER INFO, K, LDA, LWORK, M, N
10 * ..
11 * .. Array Arguments ..
12 COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
13 * ..
14 *
15 * Purpose
16 * =======
17 *
18 * ZUNGQL generates an M-by-N complex matrix Q with orthonormal columns,
19 * which is defined as the last N columns of a product of K elementary
20 * reflectors of order M
21 *
22 * Q = H(k) . . . H(2) H(1)
23 *
24 * as returned by ZGEQLF.
25 *
26 * Arguments
27 * =========
28 *
29 * M (input) INTEGER
30 * The number of rows of the matrix Q. M >= 0.
31 *
32 * N (input) INTEGER
33 * The number of columns of the matrix Q. M >= N >= 0.
34 *
35 * K (input) INTEGER
36 * The number of elementary reflectors whose product defines the
37 * matrix Q. N >= K >= 0.
38 *
39 * A (input/output) COMPLEX*16 array, dimension (LDA,N)
40 * On entry, the (n-k+i)-th column must contain the vector which
41 * defines the elementary reflector H(i), for i = 1,2,...,k, as
42 * returned by ZGEQLF in the last k columns of its array
43 * argument A.
44 * On exit, the M-by-N matrix Q.
45 *
46 * LDA (input) INTEGER
47 * The first dimension of the array A. LDA >= max(1,M).
48 *
49 * TAU (input) COMPLEX*16 array, dimension (K)
50 * TAU(i) must contain the scalar factor of the elementary
51 * reflector H(i), as returned by ZGEQLF.
52 *
53 * WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK))
54 * On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
55 *
56 * LWORK (input) INTEGER
57 * The dimension of the array WORK. LWORK >= max(1,N).
58 * For optimum performance LWORK >= N*NB, where NB is the
59 * optimal blocksize.
60 *
61 * If LWORK = -1, then a workspace query is assumed; the routine
62 * only calculates the optimal size of the WORK array, returns
63 * this value as the first entry of the WORK array, and no error
64 * message related to LWORK is issued by XERBLA.
65 *
66 * INFO (output) INTEGER
67 * = 0: successful exit
68 * < 0: if INFO = -i, the i-th argument has an illegal value
69 *
70 * =====================================================================
71 *
72 * .. Parameters ..
73 COMPLEX*16 ZERO
74 PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ) )
75 * ..
76 * .. Local Scalars ..
77 LOGICAL LQUERY
78 INTEGER I, IB, IINFO, IWS, J, KK, L, LDWORK, LWKOPT,
79 $ NB, NBMIN, NX
80 * ..
81 * .. External Subroutines ..
82 EXTERNAL XERBLA, ZLARFB, ZLARFT, ZUNG2L
83 * ..
84 * .. Intrinsic Functions ..
85 INTRINSIC MAX, MIN
86 * ..
87 * .. External Functions ..
88 INTEGER ILAENV
89 EXTERNAL ILAENV
90 * ..
91 * .. Executable Statements ..
92 *
93 * Test the input arguments
94 *
95 INFO = 0
96 LQUERY = ( LWORK.EQ.-1 )
97 IF( M.LT.0 ) THEN
98 INFO = -1
99 ELSE IF( N.LT.0 .OR. N.GT.M ) THEN
100 INFO = -2
101 ELSE IF( K.LT.0 .OR. K.GT.N ) THEN
102 INFO = -3
103 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
104 INFO = -5
105 END IF
106 *
107 IF( INFO.EQ.0 ) THEN
108 IF( N.EQ.0 ) THEN
109 LWKOPT = 1
110 ELSE
111 NB = ILAENV( 1, 'ZUNGQL', ' ', M, N, K, -1 )
112 LWKOPT = N*NB
113 END IF
114 WORK( 1 ) = LWKOPT
115 *
116 IF( LWORK.LT.MAX( 1, N ) .AND. .NOT.LQUERY ) THEN
117 INFO = -8
118 END IF
119 END IF
120 *
121 IF( INFO.NE.0 ) THEN
122 CALL XERBLA( 'ZUNGQL', -INFO )
123 RETURN
124 ELSE IF( LQUERY ) THEN
125 RETURN
126 END IF
127 *
128 * Quick return if possible
129 *
130 IF( N.LE.0 ) THEN
131 RETURN
132 END IF
133 *
134 NBMIN = 2
135 NX = 0
136 IWS = N
137 IF( NB.GT.1 .AND. NB.LT.K ) THEN
138 *
139 * Determine when to cross over from blocked to unblocked code.
140 *
141 NX = MAX( 0, ILAENV( 3, 'ZUNGQL', ' ', M, N, K, -1 ) )
142 IF( NX.LT.K ) THEN
143 *
144 * Determine if workspace is large enough for blocked code.
145 *
146 LDWORK = N
147 IWS = LDWORK*NB
148 IF( LWORK.LT.IWS ) THEN
149 *
150 * Not enough workspace to use optimal NB: reduce NB and
151 * determine the minimum value of NB.
152 *
153 NB = LWORK / LDWORK
154 NBMIN = MAX( 2, ILAENV( 2, 'ZUNGQL', ' ', M, N, K, -1 ) )
155 END IF
156 END IF
157 END IF
158 *
159 IF( NB.GE.NBMIN .AND. NB.LT.K .AND. NX.LT.K ) THEN
160 *
161 * Use blocked code after the first block.
162 * The last kk columns are handled by the block method.
163 *
164 KK = MIN( K, ( ( K-NX+NB-1 ) / NB )*NB )
165 *
166 * Set A(m-kk+1:m,1:n-kk) to zero.
167 *
168 DO 20 J = 1, N - KK
169 DO 10 I = M - KK + 1, M
170 A( I, J ) = ZERO
171 10 CONTINUE
172 20 CONTINUE
173 ELSE
174 KK = 0
175 END IF
176 *
177 * Use unblocked code for the first or only block.
178 *
179 CALL ZUNG2L( M-KK, N-KK, K-KK, A, LDA, TAU, WORK, IINFO )
180 *
181 IF( KK.GT.0 ) THEN
182 *
183 * Use blocked code
184 *
185 DO 50 I = K - KK + 1, K, NB
186 IB = MIN( NB, K-I+1 )
187 IF( N-K+I.GT.1 ) THEN
188 *
189 * Form the triangular factor of the block reflector
190 * H = H(i+ib-1) . . . H(i+1) H(i)
191 *
192 CALL ZLARFT( 'Backward', 'Columnwise', M-K+I+IB-1, IB,
193 $ A( 1, N-K+I ), LDA, TAU( I ), WORK, LDWORK )
194 *
195 * Apply H to A(1:m-k+i+ib-1,1:n-k+i-1) from the left
196 *
197 CALL ZLARFB( 'Left', 'No transpose', 'Backward',
198 $ 'Columnwise', M-K+I+IB-1, N-K+I-1, IB,
199 $ A( 1, N-K+I ), LDA, WORK, LDWORK, A, LDA,
200 $ WORK( IB+1 ), LDWORK )
201 END IF
202 *
203 * Apply H to rows 1:m-k+i+ib-1 of current block
204 *
205 CALL ZUNG2L( M-K+I+IB-1, IB, IB, A( 1, N-K+I ), LDA,
206 $ TAU( I ), WORK, IINFO )
207 *
208 * Set rows m-k+i+ib:m of current block to zero
209 *
210 DO 40 J = N - K + I, N - K + I + IB - 1
211 DO 30 L = M - K + I + IB, M
212 A( L, J ) = ZERO
213 30 CONTINUE
214 40 CONTINUE
215 50 CONTINUE
216 END IF
217 *
218 WORK( 1 ) = IWS
219 RETURN
220 *
221 * End of ZUNGQL
222 *
223 END